Problem: Multiply the following complex numbers: $({-4i}) \cdot ({-3-3i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4i}) \cdot ({-3-3i}) = $ $ ({0} \cdot {-3}) + ({0} \cdot {-3}i) + ({-4}i \cdot {-3}) + ({-4}i \cdot {-3}i) $ Then simplify the terms: $ (0) + (0i) + (12i) + (12 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 12)i + 12i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 12)i - 12 $ The result is simplified: $ (0 - 12) + (12i) = -12+12i $